Blow past the notion that biopics about genius have to be stuffy, pious, by-the-book endurance tests. Not always. The Theory of Everything gives us the real, breathing, sweating, bleeding world that British theoretical physicist and cosmologist Stephen Hawking calls his own. Challenged by a progressive neurological disease that robs him of movement and speech, Hawking nonetheless carries on, his mind racing to solve the mysteries of the universe.

I expected director James Marsh to cue the violins and hard-sell the triumph over adversity. Instead, the emotionally charged, surprisingly cheeky Theory of Everything gazes unflinchingly at the untidy, ornery humanity of a thinking, feeling, sexual being caged by his own body. Hawking is a role that demands miracles of an actor. And Eddie Redmayne, in a landmark performance, delivers them. He’s matched by Felicity Jones, who is simply sensational as Hawking’s blunt, determined wife, Jane.

It’s Jane’s book Traveling to Infinity: My Life With Stephen that serves as source material for the witty, well-observed script by Anthony McCarten. Director Marsh, whose 2008 documentary Man on Wire walked the tightrope with Philippe Petit, takes to the high wire again by refusing to reduce Hawking to a saint martyred by symptoms related to ALS (Lou Gehrig’s disease). Since Hawking wasn’t born with this affliction, Marsh and the skilled cinematographer Benoît Delhomme zap us back to 1963, with a whirling shot of Hawking – thick specs in place – biking around the Cambridge campus, his head perpetually in the clouds until meeting pretty student Jane Wilde, a poet and chorale singer with a belief in God that Hawking doesn’t share. That sight alone will be a revelation to those stuck with the image of Hawking shackled to a motorized wheelchair, his head lolling, his muscles limp, his voice computer-generated.

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For a start, The Theory of Everything is a Big Bang Theory-ish romance between two young geeks, bodies and minds colliding. And its exuberance is as bracing as it is unexpected. Hawking is just 21 when he’s diagnosed and given two years to live. It’s Jane who kicks him out of depression and into a marriage that will last 25 years and produce three children. When a friend asks Hawking how he gets it up for sex, he cracks, “That part is automatic.”

There is nothing automatic about the life Jane painstakingly builds for her husband as his condition deteriorates. Marsh is unsparing with the details. And Redmayne (Les Misérables) and Jones (Like Crazy) reach for the stars in two of the year’s best and most fearless acting feats. It’s irksome that the film treads too lightly on the couple’s divorce, partly resulting from Jane’s attraction (and later marriage) to her husband’s caretaker Jonathan Hellyer Jones (the excellent Charlie Cox). Then there’s Hawking’s 1995 marriage and 2006 split from flinty nurse Elaine Mason (Maxine Peake). These are the few instances when the film feels reticent and removed. Otherwise, The Theory of Everything, referring to Hawking’s dream of finding an equation to explain all existence, is riveting science, emotional provocation and one-of-a-kind love story all rolled into one triumphant film. Bravo.